Question 1

The energy of a molecule can normally be divided into the following categories:

Accepted Answer

A) rotational and vibrational 
B) translational,rotational and vibrational 
C) electronic,translational,rotational,and vibrational 
D) rotational 
E) electronic 
A) rotational and vibrational 
B) translational,rotational and vibrational 
C) electronic,translational,rotational,and vibrational 
D) rotational 
E) electronic

Question 2

The wave functions of some molecules are a combination of wave functions with different values of the orbital quantum number  
)The wave function of PF5 combines s,p and d states in an sp3d hybrid orbital.We would expect such an overlap of wave functions in individual molecules to represent

Accepted Answer

A) ionic bonding 
B) metallic bonding. 
C) covalent bonding. 
D) Van der Waal's bonding. 
E) hydrogen bonding. 
A) ionic bonding 
B) metallic bonding. 
C) covalent bonding. 
D) Van der Waal's bonding. 
E) hydrogen bonding.

Question 3

The moment of inertia of a CO molecule is 1.46 × 10−46 kg ⋅ m2.What is the wavelength of the photon emitted if a rotational transition occurs from the J = 3 to the J = 2 state?

Accepted Answer

A) 4.36 × 10−4 m 
B) 8.71 × 10−4 m 
C) 17.4 × 10−3 m 
D) 5.53 × 10−4 m 
E) 2.90 × 10−4 m 
A) 4.36 × 10−4 m 
B) 8.71 × 10−4 m 
C) 17.4 × 10−3 m 
D) 5.53 × 10−4 m 
E) 2.90 × 10−4 m

Question 4

In the Lennard-Jones model of the hydrogen molecule,the potential is given by  
)In this model,the minimum internuclear separation,r0,is

Accepted Answer

A)    . 
B)    . 
C)    . 
D)    . 
E)    . 
A)    . 
B)    . 
C)    . 
D)    . 
E)    .

Question 5

How many degrees of freedom does a diatomic molecule have?

Accepted Answer

A) 3 
B) 6 
C) 5 
D) 7 
E) 9 
A) 3 
B) 6 
C) 5 
D) 7 
E) 9

Question 6

The smallest object one can distinguish using the electron microscope is on the order of one nanometer (1 nm = 10−9 m).How many atoms of gold are contained in a cube whose edge is 1 nm long? The atomic mass of gold is 197 and its density is 19.3 g/cm3.

Accepted Answer

Question 7

An oxygen molecule has a moment of inertia of 5 × 10−46 kg ⋅ m2.Calculate the bond length (in nm).Recall that the atomic mass of oxygen is 16 u (1 u = 1.66 × 10−27 kg).

Accepted Answer

A) 0.3 
B) 0.1 
C) 0.2 
D) 0.4 
E) 0.5 
A) 0.3 
B) 0.1 
C) 0.2 
D) 0.4 
E) 0.5

Question 8

Because HF,hydrogen fluoride,is a covalent gaseous molecule at room temperature,we might reasonably expect that at room temperature HCl,hydrogen chloride,is

Accepted Answer

A) a covalent gaseous molecule. 
B) a covalent solid. 
C) a metallic gas. 
D) a metallic solid. 
E) an ionic solid. 
A) a covalent gaseous molecule. 
B) a covalent solid. 
C) a metallic gas. 
D) a metallic solid. 
E) an ionic solid.

Question 9

A molecule makes a transition from the J = 1 to the J = 0 rotational energy state.The wavelength of the emitted photon is 2.6 × 10−3 m.What is the moment of inertia of the molecule (in kg ⋅ m2)?

Accepted Answer

A) 2.9 × 10−46 
B) 5.7 × 10−45 
C) 1.1 × 10−44 
D) 1.5 × 10−46 
E) 9.1 × 10−46 
A) 2.9 × 10−46 
B) 5.7 × 10−45 
C) 1.1 × 10−44 
D) 1.5 × 10−46 
E) 9.1 × 10−46

Question 10

In comparing vibrational and rotational levels in molecules,we find that the energy separation between adjacent energy levels is

Accepted Answer

A) the same in rotational and vibrational levels. 
B) greater in rotational than in vibrational levels. 
C) greater in vibrational than in rotational levels. 
D) directly proportional with one rotational level for each vibrational level. 
E) inversely proportional with one rotational level for each vibrational level. 
A) the same in rotational and vibrational levels. 
B) greater in rotational than in vibrational levels. 
C) greater in vibrational than in rotational levels. 
D) directly proportional with one rotational level for each vibrational level. 
E) inversely proportional with one rotational level for each vibrational level.

Question 11

The dissociation energy of the hydrogen molecule is approximately 5 eV.What is the temperature of a monatomic molecule whose kinetic energy is equal to 5.000 eV?

Accepted Answer

A) 28990 K 
B) 57970 K 
C) 38650 K 
D) 23190 K 
E) 12880 K 
A) 28990 K 
B) 57970 K 
C) 38650 K 
D) 23190 K 
E) 12880 K

Question 12

The rotation spectrum of the HCl molecule has been observed in the far infrared,around 50 × 10−6 m.The spacing between successive lines in the spectrum corresponds to radiation of wavelength equal to 5 microns (1 μm = 10−6 m).Determine the frequency of the photon associated with this transition.

Accepted Answer

A) 6 × 1014 Hz 
B) 6 × 1012 Hz 
C) 6 × 1011 Hz 
D) 6 × 1013 Hz 
E) 6 × 1010 Hz 
A) 6 × 1014 Hz 
B) 6 × 1012 Hz 
C) 6 × 1011 Hz 
D) 6 × 1013 Hz 
E) 6 × 1010 Hz

Question 13

When calculating the rotational kinetic energy of a diatomic molecule,with atoms of mass m1 and m2,the moment of inertia about an axis passing through the molecule's center of mass,with r the atomic separation,is

Accepted Answer

A)    . 
B)    . 
C)    . 
D)    . 
E)    . 
A)    . 
B)    . 
C)    . 
D)    . 
E)    .

Question 14

An energy band in a solid consists of

Accepted Answer

A) an infinite number of levels,with each level corresponding to a point in a box. 
B) a large number of energy levels so closely spaced that they may be regarded as a continuous band. 
C) an infinite number of wave functions,with each wave function corresponding to a point in a box. 
D) a large number of electrons so closely spaced that they may be regarded as a continuous band of electric charge. 
E) an infinite number of electrons,with each electron corresponding to a point in a box. 
A) an infinite number of levels,with each level corresponding to a point in a box. 
B) a large number of energy levels so closely spaced that they may be regarded as a continuous band. 
C) an infinite number of wave functions,with each wave function corresponding to a point in a box. 
D) a large number of electrons so closely spaced that they may be regarded as a continuous band of electric charge. 
E) an infinite number of electrons,with each electron corresponding to a point in a box.

Question 15

The energy gap for a semiconductor is 1.25 eV.Of the frequencies given below,what is the minimum frequency photon than can move an electron from the valence band to the conduction band?

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 16

If an electric field is applied to a metal

Accepted Answer

A) very few electrons are excited into the conduction band. 
B) electrons having energies near the Fermi energy require only a small amount of additional energy from the applied field to reach nearby empty energy states. 
C) electrons having energies near the bottom of the band require only a small amount of additional energy from the applied field to reach nearby empty energy states. 
D) the principal mode of conduction is through the motion of holes in the filled part of the band. 
E) the Fermi energy Ef becomes equal to the applied electric field E. 
A) very few electrons are excited into the conduction band. 
B) electrons having energies near the Fermi energy require only a small amount of additional energy from the applied field to reach nearby empty energy states. 
C) electrons having energies near the bottom of the band require only a small amount of additional energy from the applied field to reach nearby empty energy states. 
D) the principal mode of conduction is through the motion of holes in the filled part of the band. 
E) the Fermi energy Ef becomes equal to the applied electric field E.

Question 17

A diatomic molecule consists of two point masses,m1 and m2,separated by a distance r.If x is the distance from m1 to the center of mass,find the moment of inertia in terms of x about an axis perpendicular to the molecular axis through the center of mass.

Accepted Answer

A) 0 
B) m1m2 r2/m1 + m2 
C) m1(r − x)2 + m2x2 
D) m1x2 + m2(r − x)2 
E) m2x2 + m1r2 
A) 0 
B) m1m2 r2/m1 + m2 
C) m1(r − x)2 + m2x2 
D) m1x2 + m2(r − x)2 
E) m2x2 + m1r2

Question 18

The Fermi energy of a metal at a temperature T is 7.0 eV.What is the average energy (in eV)of a conduction electron at that temperature?

Accepted Answer

A) 2.8 
B) 7.0 
C) 3.5 
D) 4.2 
E) 4.7 
A) 2.8 
B) 7.0 
C) 3.5 
D) 4.2 
E) 4.7

Question 19

The force constant of HCl is 480 N/m.If the atomic masses are 1 u and 35 u (1 u = 1.66 × 10−27 kg),find the fundamental frequency (in Hz).

Accepted Answer

A) 6.4 × 1013 
B) 9.2 × 1013 
C) 7.7 × 1013 
D) 8.7 × 1013 
E) 1.4 × 1013 
A) 6.4 × 1013 
B) 9.2 × 1013 
C) 7.7 × 1013 
D) 8.7 × 1013 
E) 1.4 × 1013

Question 20

The rotational kinetic energy of a diatomic molecule can take the form

Accepted Answer

A) (1/2)mω2 
B) (1/2)Iω2 
C) [m1m2/(m1 + m2)]r2ω2 
D) (1/2)mv2 
E) 1/2 μω2 
A) (1/2)mω2 
B) (1/2)Iω2 
C) [m1m2/(m1 + m2)]r2ω2 
D) (1/2)mv2 
E) 1/2 μω2

Exam 43: Molecules and Solids

The energy of a molecule can normally be divided into the following categories:

The wave functions of some molecules are a combination of wave functions with different values of the orbital quantum number )The wave function of PF5 combines s,p and d states in an sp3d hybrid orbital.We would expect such an overlap of wave functions in individual molecules to represent

The moment of inertia of a CO molecule is 1.46 × 10−46 kg ⋅ m2.What is the wavelength of the photon emitted if a rotational transition occurs from the J = 3 to the J = 2 state?

In the Lennard-Jones model of the hydrogen molecule,the potential is given by )In this model,the minimum internuclear separation,r0,is

How many degrees of freedom does a diatomic molecule have?

The smallest object one can distinguish using the electron microscope is on the order of one nanometer (1 nm = 10−9 m).How many atoms of gold are contained in a cube whose edge is 1 nm long? The atomic mass of gold is 197 and its density is 19.3 g/cm3.

An oxygen molecule has a moment of inertia of 5 × 10−46 kg ⋅ m2.Calculate the bond length (in nm).Recall that the atomic mass of oxygen is 16 u (1 u = 1.66 × 10−27 kg).

Because HF,hydrogen fluoride,is a covalent gaseous molecule at room temperature,we might reasonably expect that at room temperature HCl,hydrogen chloride,is

A molecule makes a transition from the J = 1 to the J = 0 rotational energy state.The wavelength of the emitted photon is 2.6 × 10−3 m.What is the moment of inertia of the molecule (in kg ⋅ m2)?

In comparing vibrational and rotational levels in molecules,we find that the energy separation between adjacent energy levels is

The dissociation energy of the hydrogen molecule is approximately 5 eV.What is the temperature of a monatomic molecule whose kinetic energy is equal to 5.000 eV?

When calculating the rotational kinetic energy of a diatomic molecule,with atoms of mass m1 and m2,the moment of inertia about an axis passing through the molecule's center of mass,with r the atomic separation,is

An energy band in a solid consists of

The energy gap for a semiconductor is 1.25 eV.Of the frequencies given below,what is the minimum frequency photon than can move an electron from the valence band to the conduction band?

If an electric field is applied to a metal

A diatomic molecule consists of two point masses,m1 and m2,separated by a distance r.If x is the distance from m1 to the center of mass,find the moment of inertia in terms of x about an axis perpendicular to the molecular axis through the center of mass.

The Fermi energy of a metal at a temperature T is 7.0 eV.What is the average energy (in eV)of a conduction electron at that temperature?

The force constant of HCl is 480 N/m.If the atomic masses are 1 u and 35 u (1 u = 1.66 × 10−27 kg),find the fundamental frequency (in Hz).

The rotational kinetic energy of a diatomic molecule can take the form

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The wave functions of some molecules are a combination of wave functions with different values of the orbital quantum number )The wave function of PF₅ combines s,p and d states in an sp³d hybrid orbital.We would expect such an overlap of wave functions in individual molecules to represent

The moment of inertia of a CO molecule is 1.46 × 10−⁴⁶ kg ⋅ m².What is the wavelength of the photon emitted if a rotational transition occurs from the J = 3 to the J = 2 state?

In the Lennard-Jones model of the hydrogen molecule,the potential is given by )In this model,the minimum internuclear separation,r₀,is

The smallest object one can distinguish using the electron microscope is on the order of one nanometer (1 nm = 10−⁹ m).How many atoms of gold are contained in a cube whose edge is 1 nm long? The atomic mass of gold is 197 and its density is 19.3 g/cm³.

An oxygen molecule has a moment of inertia of 5 × 10−⁴⁶ kg ⋅ m².Calculate the bond length (in nm).Recall that the atomic mass of oxygen is 16 u (1 u = 1.66 × 10−²⁷ kg).

A molecule makes a transition from the J = 1 to the J = 0 rotational energy state.The wavelength of the emitted photon is 2.6 × 10−³ m.What is the moment of inertia of the molecule (in kg ⋅ m²)?

When calculating the rotational kinetic energy of a diatomic molecule,with atoms of mass m₁ and m₂,the moment of inertia about an axis passing through the molecule's center of mass,with r the atomic separation,is

A diatomic molecule consists of two point masses,m₁ and m₂,separated by a distance r.If x is the distance from m₁ to the center of mass,find the moment of inertia in terms of x about an axis perpendicular to the molecular axis through the center of mass.

The force constant of HCl is 480 N/m.If the atomic masses are 1 u and 35 u (1 u = 1.66 × 10−²⁷ kg),find the fundamental frequency (in Hz).